勒讓德曲面之合痕與不變量

Legendrian submanifolds play a central role in the study of topology of contact and symplectic manifolds under Legendrian surgery, hence it is important to be able to distinguish them up to their Legendrian isotopy classes. One-dimensional Legendrian submanifolds are topologically knots, and have been studied intensively. In recent years the study of higher di- mensional Legendrian submanifolds is gaining more attentions. Interesting new properties of Legendrian submanifolds of dimension n 2 have been observed that will have great implications in higher dimensional contact and symplectic topology. The objective of this one-year project is to to better understand embed- ded Legendrian surfaces up to their Legendrian isotopy classes.